%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE011+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:40:02 AM UTC 2026
% Result : Theorem 5.46s 1.83s
% Output : Refutation 6.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 112 ( 36 unt; 2 def)
% Number of atoms : 219 ( 57 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 194 ( 87 ~; 78 |; 19 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn 87 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
fof(f19,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))))
& leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))))
& leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f22,plain,
? [X0,X1] :
( ( ~ leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))))
| ~ leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one) )
& test(X1)
& test(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f23,plain,
? [X0,X1] :
( ( ~ leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))))
| ~ leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one) )
& test(X1)
& test(X0) ),
inference(flattening,[],[f22]) ).
fof(f28,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f30,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f31,plain,
( ( ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))))
| ~ leq(addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))),one) )
& test(sK1)
& test(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f23]) ).
fof(f32,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one )
& ( ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f33,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one )
& ( ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one )
| ~ complement(X1,X0) ) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f30]) ).
fof(f38,plain,
test(sK0),
inference(cnf_transformation,[],[f31]) ).
fof(f39,plain,
test(sK1),
inference(cnf_transformation,[],[f31]) ).
fof(f40,plain,
( ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))))
| ~ leq(addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))),one) ),
inference(cnf_transformation,[],[f31]) ).
fof(f43,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f33]) ).
fof(f47,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f28]) ).
fof(f48,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f49,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f50,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f52,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f53,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f55,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f61,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f62,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f64,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f55]) ).
fof(f65,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1))))
| ~ leq(addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))),one) ),
inference(forward_demodulation,[],[f40,f53]) ).
fof(f66,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0))))
| ~ leq(addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))),one) ),
inference(forward_demodulation,[],[f65,f53]) ).
fof(f67,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1))),one)
| ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0)))) ),
inference(forward_demodulation,[],[f66,f53]) ).
fof(f68,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0))),one)
| ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0)))) ),
inference(forward_demodulation,[],[f67,f53]) ).
fof(f70,definition,
( spl3_1
<=> leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0)))) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f72,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0))))
| spl3_1 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f74,definition,
( spl3_2
<=> leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0))),one) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f75,plain,
( leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0))),one)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0))),one)
| spl3_2 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f68,f74,f70]) ).
fof(f87,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f43,f64]) ).
fof(f88,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f87,f53]) ).
fof(f97,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f52,f50]) ).
fof(f109,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f53,f52]) ).
fof(f149,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(superposition,[],[f53,f48]) ).
fof(f163,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f49,f62]) ).
fof(f178,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(superposition,[],[f52,f49]) ).
fof(f180,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(superposition,[],[f53,f49]) ).
fof(f274,plain,
one = addition(sK0,c(sK0)),
inference(resolution,[],[f88,f38]) ).
fof(f275,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f88,f39]) ).
fof(f456,plain,
one = addition(sK1,one),
inference(superposition,[],[f97,f275]) ).
fof(f467,plain,
one = addition(one,sK1),
inference(forward_demodulation,[],[f456,f53]) ).
fof(f1099,plain,
! [X0] : multiplication(X0,one) = addition(X0,multiplication(X0,sK1)),
inference(superposition,[],[f163,f467]) ).
fof(f1170,plain,
! [X0] : addition(X0,multiplication(X0,sK1)) = X0,
inference(forward_demodulation,[],[f1099,f62]) ).
fof(f1483,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(superposition,[],[f49,f180]) ).
fof(f2252,plain,
! [X2,X3,X0,X1] : addition(multiplication(X1,addition(X3,X2)),multiplication(X0,X2)) = addition(multiplication(X1,X3),multiplication(addition(X0,X1),X2)),
inference(superposition,[],[f178,f149]) ).
fof(f3009,plain,
! [X0,X1] : addition(X1,X0) = addition(X0,addition(multiplication(X0,sK1),X1)),
inference(superposition,[],[f109,f1170]) ).
fof(f3818,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(one,sK0))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f76,f275]) ).
fof(f3820,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(c(sK0),c(sK1)),multiplication(addition(sK0,c(sK0)),sK1))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f3818,f109]) ).
fof(f3822,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(c(sK0),addition(c(sK1),sK1)),multiplication(sK0,sK1))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f3820,f2252]) ).
fof(f3824,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),addition(c(sK1),sK1)))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f3822,f53]) ).
fof(f3826,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),addition(sK1,c(sK1))))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f3824,f1483]) ).
fof(f3828,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),one))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f3826,f275]) ).
fof(f3830,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),c(sK0))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f3828,f62]) ).
fof(f3832,plain,
( ~ leq(addition(c(sK0),addition(multiplication(one,sK0),multiplication(sK0,sK1))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f3830,f109]) ).
fof(f3851,plain,
( ~ leq(addition(c(sK0),addition(sK0,multiplication(sK0,sK1))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f3832,f61]) ).
fof(f3855,plain,
( ~ leq(addition(sK0,addition(multiplication(sK0,sK1),c(sK0))),one)
| spl3_2 ),
inference(forward_demodulation,[],[f3851,f109]) ).
fof(f3859,plain,
( ~ leq(addition(c(sK0),sK0),one)
| spl3_2 ),
inference(forward_demodulation,[],[f3855,f3009]) ).
fof(f3863,plain,
( ~ leq(addition(sK0,c(sK0)),one)
| spl3_2 ),
inference(forward_demodulation,[],[f3859,f53]) ).
fof(f3865,plain,
( ~ leq(one,one)
| spl3_2 ),
inference(forward_demodulation,[],[f3863,f274]) ).
fof(f3868,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(one,sK0))))
| spl3_1 ),
inference(forward_demodulation,[],[f72,f275]) ).
fof(f3872,plain,
( ~ leq(one,addition(multiplication(one,sK0),addition(multiplication(c(sK0),c(sK1)),multiplication(addition(sK0,c(sK0)),sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f3868,f109]) ).
fof(f3875,plain,
( ~ leq(one,addition(multiplication(one,sK0),addition(multiplication(c(sK0),addition(c(sK1),sK1)),multiplication(sK0,sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f3872,f2252]) ).
fof(f3877,plain,
( ~ leq(one,addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),addition(c(sK1),sK1)))))
| spl3_1 ),
inference(forward_demodulation,[],[f3875,f53]) ).
fof(f3887,plain,
( ~ leq(one,addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),addition(sK1,c(sK1))))))
| spl3_1 ),
inference(forward_demodulation,[],[f3877,f1483]) ).
fof(f3888,plain,
( ~ leq(one,addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),one))))
| spl3_1 ),
inference(forward_demodulation,[],[f3887,f275]) ).
fof(f3889,plain,
( ~ leq(one,addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),c(sK0))))
| spl3_1 ),
inference(forward_demodulation,[],[f3888,f62]) ).
fof(f3890,plain,
( ~ leq(one,addition(c(sK0),addition(multiplication(one,sK0),multiplication(sK0,sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f3889,f109]) ).
fof(f3891,plain,
( ~ leq(one,addition(c(sK0),addition(sK0,multiplication(sK0,sK1))))
| spl3_1 ),
inference(forward_demodulation,[],[f3890,f61]) ).
fof(f3892,plain,
( ~ leq(one,addition(sK0,addition(multiplication(sK0,sK1),c(sK0))))
| spl3_1 ),
inference(forward_demodulation,[],[f3891,f109]) ).
fof(f3893,plain,
( ~ leq(one,addition(c(sK0),sK0))
| spl3_1 ),
inference(forward_demodulation,[],[f3892,f3009]) ).
fof(f3894,plain,
( ~ leq(one,addition(sK0,c(sK0)))
| spl3_1 ),
inference(forward_demodulation,[],[f3893,f53]) ).
fof(f3895,plain,
( ~ leq(one,one)
| spl3_1 ),
inference(forward_demodulation,[],[f3894,f274]) ).
fof(f3909,plain,
( one != addition(one,one)
| spl3_2 ),
inference(resolution,[],[f3865,f47]) ).
fof(f3910,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f3909,f50]) ).
fof(f3911,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f3910]) ).
fof(f3912,plain,
( leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(one,sK0))),one)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f75,f275]) ).
fof(f3913,plain,
( leq(addition(multiplication(one,sK0),addition(multiplication(c(sK0),c(sK1)),multiplication(addition(sK0,c(sK0)),sK1))),one)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f3912,f109]) ).
fof(f3914,plain,
( leq(addition(multiplication(one,sK0),addition(multiplication(c(sK0),addition(c(sK1),sK1)),multiplication(sK0,sK1))),one)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f3913,f2252]) ).
fof(f3915,plain,
( leq(addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),addition(c(sK1),sK1)))),one)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f3914,f53]) ).
fof(f3916,plain,
( leq(addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),addition(sK1,c(sK1))))),one)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f3915,f1483]) ).
fof(f3917,plain,
( leq(addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),one))),one)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f3916,f275]) ).
fof(f3918,plain,
( leq(addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),c(sK0))),one)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f3917,f62]) ).
fof(f3919,plain,
( leq(addition(c(sK0),addition(multiplication(one,sK0),multiplication(sK0,sK1))),one)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f3918,f109]) ).
fof(f3920,plain,
( leq(addition(c(sK0),addition(sK0,multiplication(sK0,sK1))),one)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f3919,f61]) ).
fof(f3921,plain,
( leq(addition(sK0,addition(multiplication(sK0,sK1),c(sK0))),one)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f3920,f109]) ).
fof(f3922,plain,
( leq(addition(c(sK0),sK0),one)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f3921,f3009]) ).
fof(f3923,plain,
( leq(addition(sK0,c(sK0)),one)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f3922,f53]) ).
fof(f3924,plain,
( leq(one,one)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f3923,f274]) ).
fof(f3925,plain,
( $false
| spl3_1
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f3924,f3895]) ).
fof(f3926,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[],[f3925]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f77]) ).
cnf(s24,plain,
spl3_2,
inference(sat_conversion,[],[f3911]) ).
cnf(s25,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f3926]) ).
cnf(s26,plain,
spl3_1,
inference(rat,[],[s25,s24]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s1,s24,s26]) ).
fof(f3927,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE011+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n003.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 13:00:11 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.46/1.83 % (515121)Detected formulas, will run a generic FOF schedule.
% 5.46/1.83 % (515202)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3275185875:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.46/1.83 % (515198)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2775425507:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.46/1.83 % (515208)dis-21_1_sil=8000:lcm=predicate:random_seed=4104473839:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 5.46/1.83 % (515204)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1599710218:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.46/1.83 % (515205)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3095558257:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.46/1.83 % (515200)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2185017867:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.46/1.83 % (515206)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3915113585:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.46/1.83 % (515204)Refutation not found, incomplete strategy
% 5.46/1.83 % (515204)------------------------------
% 5.46/1.83 % (515204)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.83 % (515204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.83 % (515204)CaDiCaL version: 2.1.3
% 5.46/1.83 % (515204)Termination reason: Refutation not found, incomplete strategy
% 5.46/1.83 % (515204)Time elapsed: 0.002 s
% 5.46/1.83 % (515204)Peak memory usage: 89 MB
% 5.46/1.83 % (515204)Instructions burned: 2 (million)
% 5.46/1.83 % (515208)Refutation not found, incomplete strategy
% 5.46/1.83 % (515208)------------------------------
% 5.46/1.83 % (515208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.83 % (515208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.83 % (515208)CaDiCaL version: 2.1.3
% 5.46/1.83 % (515208)Termination reason: Refutation not found, incomplete strategy
% 5.46/1.83 % (515208)Time elapsed: 0.002 s
% 5.46/1.83 % (515208)Peak memory usage: 88 MB
% 5.46/1.83 % (515208)Instructions burned: 2 (million)
% 5.46/1.83 % (515205)Instruction limit reached!
% 5.46/1.83 % (515205)------------------------------
% 5.46/1.83 % (515205)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.83 % (515205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.83 % (515205)CaDiCaL version: 2.1.3
% 5.46/1.83 % (515205)Termination reason: Instruction limit
% 5.46/1.83 % (515205)Termination phase: Saturation
% 5.46/1.83 % (515205)Time elapsed: 0.069 s
% 5.46/1.83 % (515205)Peak memory usage: 89 MB
% 5.46/1.83 % (515205)Instructions burned: 121 (million)
% 5.46/1.83 % (515206)Instruction limit reached!
% 5.46/1.83 % (515206)------------------------------
% 5.46/1.83 % (515206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.83 % (515206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.83 % (515206)CaDiCaL version: 2.1.3
% 5.46/1.83 % (515206)Termination reason: Instruction limit
% 5.46/1.83 % (515206)Termination phase: Saturation
% 5.46/1.83 % (515206)Time elapsed: 0.081 s
% 5.46/1.83 % (515206)Peak memory usage: 90 MB
% 5.46/1.83 % (515206)Instructions burned: 140 (million)
% 5.46/1.83 % (515249)lrs+10_1_sil=8000:sp=occurrence:random_seed=2328355937:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.46/1.83 % (515250)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1376276034:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.46/1.83 % (515204)------------------------------
% 5.46/1.83 % (515204)------------------------------
% 5.46/1.83 % (515208)------------------------------
% 5.46/1.83 % (515208)------------------------------
% 5.46/1.83 % (515250)Instruction limit reached!
% 5.46/1.83 % (515250)------------------------------
% 5.46/1.83 % (515250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.83 % (515250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.83 % (515250)CaDiCaL version: 2.1.3
% 5.46/1.83 % (515250)Termination reason: Instruction limit
% 5.46/1.83 % (515250)Termination phase: Saturation
% 5.46/1.83 % (515250)Time elapsed: 0.101 s
% 5.46/1.83 % (515250)Peak memory usage: 90 MB
% 5.46/1.83 % (515250)Instructions burned: 158 (million)
% 5.46/1.83 % (515295)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=796061818:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 5.46/1.83 % (515294)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1242239339:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 5.46/1.83 % (515249)Instruction limit reached!
% 5.46/1.83 % (515249)------------------------------
% 5.46/1.83 % (515249)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.83 % (515249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.83 % (515249)CaDiCaL version: 2.1.3
% 5.46/1.83 % (515249)Termination reason: Instruction limit
% 5.46/1.83 % (515249)Termination phase: Saturation
% 5.46/1.83 % (515249)Time elapsed: 0.176 s
% 5.46/1.83 % (515249)Peak memory usage: 91 MB
% 5.46/1.83 % (515249)Instructions burned: 285 (million)
% 5.46/1.83 % (515302)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1570160144:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.46/1.83 % (515294)First to succeed.
% 5.46/1.83 % (515294)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-515121"
% 5.46/1.83 % (515305)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=679106741:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.46/1.83 % (515295)Instruction limit reached!
% 5.46/1.83 % (515295)------------------------------
% 5.46/1.83 % (515295)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.83 % (515295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.83 % (515295)CaDiCaL version: 2.1.3
% 5.46/1.83 % (515295)Termination reason: Instruction limit
% 5.46/1.83 % (515295)Termination phase: Saturation
% 5.46/1.83 % (515295)Time elapsed: 0.154 s
% 5.46/1.83 % (515295)Peak memory usage: 92 MB
% 5.46/1.83 % (515295)Instructions burned: 249 (million)
% 5.46/1.83 % (515302)Instruction limit reached!
% 5.46/1.83 % (515302)------------------------------
% 5.46/1.83 % (515302)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.83 % (515302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.83 % (515302)CaDiCaL version: 2.1.3
% 5.46/1.83 % (515302)Termination reason: Instruction limit
% 5.46/1.83 % (515302)Termination phase: Saturation
% 5.46/1.83 % (515302)Time elapsed: 0.182 s
% 5.46/1.83 % (515302)Peak memory usage: 90 MB
% 5.46/1.83 % (515302)Instructions burned: 294 (million)
% 5.46/1.83 % (515308)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=905927936:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.46/1.83 % (515294)Refutation found. Thanks to Tanya!
% 5.46/1.83 % SZS status Theorem for theBenchmark
% 5.46/1.83 % SZS output start Proof for theBenchmark
% See solution above
% 6.66/2.02 % (515294)------------------------------
% 6.66/2.02 % (515294)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.66/2.02 % (515294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.66/2.02 % (515294)CaDiCaL version: 2.1.3
% 6.66/2.02 % (515294)Termination reason: Refutation
% 6.66/2.02 % (515294)Time elapsed: 0.085 s
% 6.66/2.02 % (515294)Peak memory usage: 91 MB
% 6.66/2.02 % (515294)Instructions burned: 137 (million)
% 6.66/2.02 % (515294)------------------------------
% 6.66/2.02 % (515294)------------------------------
% 6.66/2.02 % (515121)Success in time 0.844 s
% 6.66/2.02 % Vampire exiting
%------------------------------------------------------------------------------